A Note on the Take-home Assignment
The assignment says:
The probability of the phillinx failing is given by a standardized Normal Distribution, so , if z represents
the life of the Phillinx, the probability of the phillinx failing last year is Pz  0 , the probability of it failing
this year is P0  z  1 and the probability of it lasting into the Ever After is Pz  1 .
This is the distribution z ~ N 0,1 that you used on the first page of exam 3 and which is explained in
251disrtex2. You use exactly what it says.
The assignment then says:
The probability of the Flubberall failing is given by a Continuous Uniform Distribution, where c  1 and
d  2  f , where f is the fourth digit of your student number, divided by 10. For example if Seymour’s
student number is 012345, his value of d  2  .3  2.3 . If the fourth digit of your student number is zero,
use d  3.1 . If x represents the life of the Flubberall, the probability of the Flubberall failing last year is
Px  0 , the probability of it failing this year is P0  x  1 and the probability of it lasting into the Ever
After is Px  1 .
This is the Continuous Uniform Distribution with an example in 251solnL3 and a description in
251probex3.
You now have 3 probabilities for each component or a total of 3 times 3 = 9 joint events. Each joint event
has a probability found by multiplying component probabilities together. Each joint event will down the
machine at a certain time. For example, if F2 is the chance that component 1 fails in period 2 (this year)
and Ph3 is the chance that component 2 fails in period 3 (Ever After), the event F2  Ph3 has a
probability found by multiplying the probability that component 2 fails in period 2 and the probability that
component 1 fails in period 3. Because the machine fails when the last component fails this is an event that
downs the machine in period 3. There are others, and the probability that the machine fails in period 3 is the
sum of the probabilities of the events that will down the machine in period 3.
Problem H4, which I went through in class and has a posted solution is an example of how to do this for 4
periods – it’s lots easier to do this for 3.